C4.15. FMS Subroutine XXDWTP

RSDWTP
RNDWTP

PURPOSE: Weighted Matrix Triple Product and Sum

Compute the matrix triple product, multiply it by a scalar and add it to a matrix:

[S] = [S] + W{B}T[D]{B} (Symmetric)
[S] = [S] + W{B}T[D]{A} (Nonsymmetric)

SYNOPSIS


	CALL RSDWTP (W, B, D, S, N, M)

	CALL RNDWTP (W, B, D, A, S, N, M)

INPUT PARAMETERS:

W = Real.
Scale Factor.
B(N,M) = Real array.
Matrix stored by columns.
D(N,N) = Real array.
Full matrix stored by columns. For symmetric problems (RSDWTP), [D] must be symmetric.
A(N,M) = Real array (RNDWTP only).
Matrix stored by columns.
N = Integer.
Number of rows in matrix [B] and [A] and the size of the square matrix [D] . The maximum value of N must be less than or equal to 32. This restriction on N results from the use of high-speed internal registers that store intermediate values for this calculation. For most problems, N is in the range 3 to 6.
M = Integer.
Number of columns in matrix [B] and [A].

OUTPUT PARAMETERS:

S(M*(M+1)/2) = Real array (RSDWTP).
S(M,M) = Real array (RNDWTP).
For symmetric problems (RSDWTP), [S] is a lower triangular matrix stored by rows. For nonsymmetric problems, standard FORTRAN storage is used for [S].

DESCRIPTION:

This subroutine performs the matrix triple product that is typically used in finite element matrix generation. Before the first call in each element, the matrix values in [S] must be initialized to [0]. The matrix [B] is assumed full to provide for formulations including large deformation. If possible, the columns of matrix [B] should be ordered by increasing global equation number. This ordering produces a matrix [S] that is also ordered by increasing equation number and may be assembled into the global system with minimal computation. The matrix [D] is also full, which provides for orthotropic and rotated material relationships.

For symmetric problems (RSDWTP), the calculation performed is equivalent to the following FORTRAN statements.

        LS = 0
        DO I=1,M
           DO J=1,I
              LS = LS  +  1
              DO K=1,N
                 DO L=1,N
                    S(LS) = S(LS) + W*B(K,I)*D(K,L)*B(L,J)
                 END DO
              END DO
           END DO
        END DO

For nonsymmetric problems (RNDWTP), the calculation performed is equivalent to the following FORTRAN statements:

        DO I=1,M
           DO J=1,I
              DO K=1,N
                 DO L=1,N
                    S(I,J) = S(I,J) + W*B(K,I)*D(K,L)*A(L,J)
                 END DO
              END DO
           END DO
        END DO